What is the integral of 5xsin(3x) ?

The integral of 5xsin(3x) is 5(-1/3 xcos(3x)+1/9 sin(3x))+C

Popular >

integral of 5xsin(3x)

\int 5 x sin (3 x) d x

5 (- \frac{1}{3} x cos (3 x) + \frac{1}{9} sin (3 x)) + C

Solution steps

\int 5 x sin (3 x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int x sin (3 x) d x

Apply Integration By Parts

: - \frac{1}{3} x cos (3 x) - \int - \frac{1}{3} cos (3 x) d x

= 5 (- \frac{1}{3} x cos (3 x) - \int - \frac{1}{3} cos (3 x) d x)

\int - \frac{1}{3} cos (3 x) d x = - \frac{1}{9} sin (3 x)

= 5 (- \frac{1}{3} x cos (3 x) - (- \frac{1}{9} sin (3 x)))

Simplify

= 5 (- \frac{1}{3} x cos (3 x) + \frac{1}{9} sin (3 x))

Add a constant to the solution

= 5 (- \frac{1}{3} x cos (3 x) + \frac{1}{9} sin (3 x)) + C

\int \frac{cos ( x )}{1 - ( cos ( x ) ) ^{2}} d x

\int 4 x (1 - x^{2}) d x

\int \frac{1}{( 2 x + 1 ) 4 x ^{2} + 4 x - 3} d x

\int \frac{1}{( 1 + y ^{2} ) ^{2}} d y

\int - 27 e^{x} d x

What is the integral of 5xsin(3x) ?
The integral of 5xsin(3x) is 5(-1/3 xcos(3x)+1/9 sin(3x))+C